Question

Si $\angle A = 20^\circ$ y $\angle AFG =\angle AGF,$ entonces $\angle B+\angle D =$

If $\angle A = 20^\circ$ and $\angle AFG =\angle AGF,$ then $\angle B+\angle D =$

$48^\circ$

$60^\circ$

$72^\circ$

$80^\circ$

$90^\circ$

En $\triangle AFG$ , los dos ángulos de la base son iguales y $\angle A=20^\circ$ , así que

$\begin{aligned} \angle AFG &= \angle AGF \\ &= \frac{180^\circ-20^\circ}{2} \\ &= 80^\circ. \end{aligned}$

Como $\angle AFG$ y $\angle BFD$ forman un ángulo llano, $\angle BFD=100^\circ$ .

En $\triangle BFD$ , $\angle B+\angle D=180^\circ-100^\circ=80^\circ$ .

Así, D es la respuesta correcta.

In $\triangle AFG$ , the two base angles are equal and $\angle A=20^\circ$ , so

$\begin{aligned} \angle AFG &= \angle AGF \\ &= \frac{180^\circ-20^\circ}{2} \\ &= 80^\circ. \end{aligned}$

Since $\angle AFG$ and $\angle BFD$ form a straight angle, $\angle BFD=100^\circ$ .

In $\triangle BFD$ , $\angle B+\angle D=180^\circ-100^\circ=80^\circ$ .

Thus, D is the correct answer.